A spherical hole is made in a solid sphere of radius $R$ . The mass of the sphere before hollowing was $M$ . The gravitational field at the centre of the hole due to the remaining mass is -

Question

A spherical hole is made in a solid sphere of radius R . The mass of the sphere before hollowing was M . The gravitational field at the centre of the hole due to the remaining mass is -

TestHub · Accepted Answer

By the principle of superposition of fields

$\vec{E} = \vec{E_{1}} + \vec{E_{2}}$

Here, $\vec{E} = n e t f i e l d a t t h e c e n t r e o f h o l e d u e t o e n t i r e m a s s$

$\vec{E_{1}} = f i e l d d u e t o r e m a i n i n g m a s s$

and $\vec{E_{2}} = f i e l d d u e t o m a s s i n h o l e = 0$

$∴ \vec{E_{1}} = \vec{E} = (\frac{G M}{R^{3}}) . r$

where $r = \frac{R}{2}$

$∴ \vec{E} = \frac{G M}{2 R^{2}}$

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